The invention relates generally to signal analysis systems or test and measurement systems, and more particularly to a system and method for analyzing order components of a signal generated by a physical system (e.g., a mechanical system containing one or more rotating elements).
Scientists and engineers often use test and measurement systems and data acquisition systems to perform a variety of functions, including laboratory research, process monitoring and control, data logging, analytical chemistry, test and analysis of physical phenomena and analysis or control of mechanical or electrical machinery, to name a few examples. One example of hardware to implement such measuring systems is a computer-based measurement system or data acquisition (DAQ) system. Another example of a measurement system is a dedicated instrument, such as a dedicated oscilloscope or signal analyzer.
A measurement system typically may include transducers for measuring and/or providing electrical signals, signal conditioning hardware which may perform amplification, isolation and/or filtering, and measurement or DAQ hardware for receiving digital and analog signals and providing them to a processing system, such as a processor or personal computer. The computer-based measurement system or dedicated instrument may further include analysis hardware and software for analyzing and appropriately displaying the measured data.
One example where measurement and data acquisition systems are used is in the field of rotating machinery analysis. This involves the analysis of physical signals such as vibration or acoustic signals from a rotating machine. A physical signal acquired from a rotating machine may be sampled or digitized. Typically, samples of the physical signal are equidistant in time. However, rotating machines generate signals which are periodic with respect to shaft rotation, i.e., rotation angle of an underlying rotating element (e.g. a crank shaft of an engine). These rotation-periodic signals are referred to herein as order components. When the rotation rate changes in time, the order components change correspondingly in frequency. For example, when the rotation rate increases, the order components increase in frequency. Thus, a traditional analysis method such as the Discrete Fourier Transform (DFT), when applied to the physical signal, displays a frequency smearing of order components. The frequency smearing makes it very difficult to derive meaningful information about the order components. Thus, traditional signal analysis methods such as the Fourier Transform of the time domain input signal are not well suited for analyzing order components generated by rotating machines.
In order to better analyze the performance and characteristics of rotating machines, certain prior art systems convert the time-samples, i.e., the samples of the physical signal which are equally spaced in time, to angle-samples, i.e. samples which are equally spaced in shaft angle. For example, U.S. Pat. No. 4,912,661 assigned to Hewlett-Packard discloses an interpolation method for estimating angle-samples from time-samples. The method disclosed in U.S. Pat. No. 4,912,661 performs an interpolation of the time domain signal, followed by a decimation, in order to produce samples equally spaced with respect to shaft angle. The order components may then be analyzed by performing a traditional analysis method such as the Discrete Fourier Transform on the angle-samples. However, this method is expensive in terms of computational resources and may not be very accurate.
One prior art system known as the Vold-Kalman filter, developed by Bruel and Kjaer, allows the user to track the frequency of an order component given a sufficiently accurate model, i.e., a stochastic model, for the physical signal. The Vold-Kalman filter performance may be strongly sensitive to model accuracy. In other words, the tracking performance is likely to be degraded when an inaccurate signal model is supplied to the filter. Furthermore, the Vold-Kalman filter provides no mechanism for the user to evaluate the accuracy of the frequency tracking for an order component.
Therefore, there exists a need for a system and method which could more accurately and robustly analyze order components of a physical signal, and reconstruct desired order components in the time-domain.
One embodiment of the present invention comprises a signal analysis system (or measurement system) and method for analyzing an input signal acquired from a physical or mechanical system. The mechanical system may include at least one rotating apparatus. The signal analysis system may be configured to: (a) receive samples of the input signal, (b) perform an invertible joint time-frequency transform (e.g., a Gabor transform) on the samples of the input signal to produce an initial array of coefficients which depend on time and frequency, (c) generate a modified array of coefficients from the initial array of coefficients, (d) generate a time domain signal from the modified array of coefficients, e.g., by performing an inverse joint time-frequency transform on the modified array of coefficients, and (e) present the time domain signal to a user on a presentation device. The input signal is preferably a time domain input signal, i.e., the samples are sampled in time, preferably uniformly in time.
The joint time-frequency transform is invertible, meaning that any time-domain input signal (or an approximation thereto) may recovered from its transform array by applying an inverse transform to the transform array. The invertible joint time-frequency transform is preferably the Gabor transform, but may instead be a wavelet transform, or the Gabor spectrogram.
The operation (c) of generating a modified array of coefficients may comprise (1) determining (i.e. selecting) a subset of coefficient positions (i.e. time-frequency index positions) from the initial array which correspond to a desired subset of one or more order components in the input signal, and (2) setting coefficients of the modified array equal to zero at coefficient positions other than on the determined subset. The coefficients of the modified array at the subset of coefficient positions may be set equal to the corresponding coefficients of the initial array.
The input signal may comprise a plurality of order components. According to one embodiment of the present invention, various order components of the input signal may be selectively extracted (or removed) from the input signal by appropriate selection of the subset of coefficient positions from the initial array of time-frequency coefficients (i.e. the joint time-frequency representation). The inverse joint time-frequency transform may be applied to the modified array of coefficients to produce a time domain signal containing only the selected order components (or the original input signal minus the selected order components).
The subset of order components which the user desires to analyze (i.e. desires to extract from the input signal for presentation to the user) may be selected in a direct or indirect fashion. For example, the user may directly select the desired subset of one or more order components. In this case, the subset of coefficient positions corresponds to this directly-selected subset of order components. Alternatively, the user may select a second subset of one or more order components for removal from the input signal. In this case, the desired subset of order components is the complement of the second subset. The subset of coefficient positions still corresponds to the desired subset of order components. However, the desired subset has been indirectly selected by selecting the second subset of order components for removal.
Various methods may be used to select the order components of interest. For example, the signal analysis system may display a visual representation of the initial array of coefficients, where the various order components are visible in the visual representation as time-frequency order curves. The user may select one or more points in the visual representation to select one or more order components. For example, the user may position a xe2x80x9ccross-hairsxe2x80x9d on the selected order components (i.e. time-frequency order curves) in the visual representation. The signal analysis system may then determine the one or more time-frequency order curves corresponding to the selected points, where the determined time-frequency order curves correspond to the selected order components. The signal analysis system may select the subset of coefficient positions as those coefficient positions which reside in a union of time-frequency neighborhoods containing the one or more determined time-frequency order curves respectively. Alternatively, where the user (or the system) selects one or more order components for removal from the input signal, the signal analysis system may select the subset of coefficient positions as those coefficient positions which reside in the complement of the union of neighborhoods containing the selected time-frequency order curves.
The size of each neighborhood may be determined automatically or in response to user input. For example, the signal analysis system may automatically determine a size for the time-frequency neighborhood based on an estimate of minimum order distance to nearest neighbor order components.
The signal analysis system may generate the modified array of coefficients from the initial array by performing a masking operation, i.e. by constructing an order mask array, and applying the order mask array to the initial array of coefficients. The signal analysis system may determine one or more time-frequency curves which correspond to the desired subset of order components, and construct the order mask array by setting coefficients of the order mask array equal to one in a union of neighborhoods containing the one or more time-frequency curves respectively, and zero elsewhere.
Alternatively, the signal analysis system may determine a second subset of one or more time-frequency curves which define the complement of the desired subset of order components. The signal analysis system may set coefficients of the order mask array equal to zero in a union of neighborhoods respectively containing the one or more time-frequency curves of the second subset, and equal to one otherwise. Thus, the desired subset of order components (i.e. desired for extraction from the input signal and presentation to the user) comprises order components of the input signal which do not correspond to the second subset of order curves.
In one set of embodiments, the signal analysis system may compute an instantaneous rotation frequency signal which describes the instantaneous rate of change of rotation angle of the rotating apparatus with respect to time. The instantaneous rotation frequency signal defines the fundamental order component (i.e. the order component of order one) of the input signal. The order mask array may be constructed using one or more multiples of the instantaneous rotation frequency signal.
The signal analysis system may receive a rotation indicator signal indicative of rotations of the rotating apparatus, and the instantaneous rotation frequency signal may be computed in response to the rotation indicator signal. Alternatively, the signal analysis system may estimate the instantaneous rotation frequency based on a search of the initial array of transform coefficients or in response to user inputs, thus obviating the necessity of acquiring the rotation indicator signal.
The rotation indicator signal may provide an indication of each rotation of the rotating apparatus. For example, the rotation indicator signal may comprise a series of pulses where each pulse represents a complete rotation of the rotating apparatus. Signal analysis system (or a separate data acquisition device) may preprocess the rotation indicator signal to generate a series of pulse arrival times. Thus, each arrival time corresponds to a rotation of the rotating apparatus. The signal analysis system may filter the arrival times with an FIR filter to determine a stream of first derivative estimates. The coefficients of the FIR filter are determined by at least partially solving a linear system which arises from a Taylor series expansion of time with respect to rotation angle of the rotating apparatus. It may be assumed that the rotating apparatus increases in rotation angle by a fixed amount (e.g. one rotation =360 degrees) between successive arrival times.
The linear system has the form b=Gd, where b is a vector of time differences tk+nxe2x88x92tk between adjacent arrival times tk+n and a current arrival time tk, where d is a vector of unknown derivatives, i.e. the first through Mth derivatives of time with respect to angle at arrival time tk. The coefficients of the linear system, i.e. of matrix G, have the form                     (                  n          ⁢                      xe2x80x83                    ⁢          Δθ                )            k              k      !        ,
where index k ranges from 1 to the upper limit M, where index k ranges through a set of M distinct integer values different from zero, and xcex94xcex8 is a constant. In one embodiment, M is even and the set of M distinct integers comprises the non-zero integer values between xe2x88x92M/2 and M/2 inclusive.
It is noted that the linear system b=Gd need not be solved completely. In one embodiment, only the first derivative term of vector d is solved for by a series of row operations since the solution expression for first derivative term specifies the formula for the FIR filter.
The linear system b=Gd may be solved (or at least partially solved as noted above) in an offline computation. The resulting FIR filter coefficients may be stored in a memory of the signal analysis system. It is noted that a computer device separate from the signal analysis system may solve the linear system, and transfer the resulting coefficients to the signal analysis system.
In response to the stream of first derivative estimates generated by the FIR filter, the signal analysis system may (a) compute an instantaneous rotation frequency signal, and (b) multiply the instantaneous rotation frequency signal by one or more order numbers to determine one or more order curves. The one or more order numbers may be determined by or in response to user input.
The subset of coefficient positions from the initial array may be determined as those positions which reside in a union of time-frequency neighborhoods respectively containing the one or more order curves. Alternatively, the subset of coefficient positions may comprise coefficient positions which correspond to the complement of the union of the time-frequency neighborhoods respectively containing the one or more order curves. As described above, signal analysis system may generate the modified array of coefficients based on the subset of coefficient positions, and generate a time domain signal from the modified array of coefficients. The time domain signal is presented to a user on a presentation device (e.g. an audio speaker and/or display screen).
The signal analysis system may compute the instantaneous rotation frequency signal by: reciprocating the stream of derivative values to generate first rotation frequency values, and interpolating the first rotation frequency values to determine second rotation frequency values at a series of sample times, i.e. the sample times of the input signal.
In one embodiment, the signal analysis system is configured to generate the modified array of coefficients by multiplying the initial array by an arbitrary scaling array. The scaling array may be configured to emphasize and/or de-emphasize order components. The user may determine the scaling properties of the scaling function.
The user may select various different order components for analysis, e.g., in an iterative fashion. Time domain signals generated in response to the selected order components may be visually displayed and/or audially presented to the user. The user may then analyze the different order components to determine information regarding operation of the mechanical system. In response to this analysis, the user may then adjust the mechanical system in various ways. For example, the user or the system may change a design of the mechanical system, the user may replace one or more components of the mechanical system, the user or the system may predict a failure of one or more components of the mechanical system, or the user may add varying amounts of a sound-absorbent material to one or more locations of the mechanical system, etc.